Quantum Logarithmic Space and Post-Selection

Authors François Le Gall, Harumichi Nishimura , Abuzer Yakaryılmaz

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Author Details

François Le Gall
  • Graduate School of Mathematics, Nagoya University, Japan
Harumichi Nishimura
  • Graduate School of Informatics, Nagoya University, Japan
Abuzer Yakaryılmaz
  • Center for Quantum Computer Science, University of Latvia, Rīga, Latvia
  • QWorld Association, Tallinn, Estonia


We thank the anonymous reviewers of TQC 2021 for helpful comments.

Cite AsGet BibTex

François Le Gall, Harumichi Nishimura, and Abuzer Yakaryılmaz. Quantum Logarithmic Space and Post-Selection. In 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 197, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Post-selection, the power of discarding all runs of a computation in which an undesirable event occurs, is an influential concept introduced to the field of quantum complexity theory by Aaronson (Proceedings of the Royal Society A, 2005). In the present paper, we initiate the study of post-selection for space-bounded quantum complexity classes. Our main result shows the identity PostBQL = PL, i.e., the class of problems that can be solved by a bounded-error (polynomial-time) logarithmic-space quantum algorithm with post-selection (PostBQL) is equal to the class of problems that can be solved by unbounded-error logarithmic-space classical algorithms (PL). This result gives a space-bounded version of the well-known result PostBQP = PP proved by Aaronson for polynomial-time quantum computation. As a by-product, we also show that PL coincides with the class of problems that can be solved by bounded-error logarithmic-space quantum algorithms that have no time bound.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum computation theory
  • computational complexity
  • space-bounded quantum computation
  • post-selection


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